Congruence properties for the partition function

AUTOR(ES)

Ahlgren, Scott

FONTE

The National Academy of Sciences

RESUMO

Eighty years ago, Ramanujan conjectured and proved some striking congruences for the partition function modulo powers of 5, 7, and 11. Until recently, only a handful of further such congruences were known. Here we report that such congruences are much more widespread than was previously known, and we describe the theoretical framework that appears to explain every known Ramanujan-type congruence.

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